A281992 - OEIS

%I #13 Jun 02 2024 14:04:53

%S 2,3,4,9,12,19,48,54,90,97,104,174,349,385,1020,1294,1737,2430,9040,

%T 14173,15604,17943,37447,149803,164043

%N Numbers k such that (2*10^k - 143)/3 is prime.

%C For k > 1, numbers k such that k-2 occurrences of the digit 6 followed by the digits 19 is prime (see Example section).

%C a(26) > 2*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 6w19</a>.

%e 3 is in this sequence because (2*10^3 - 143)/3 = 619 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 19;

%e a(2) = 3, 619;

%e a(3) = 4, 6619;

%e a(4) = 9, 666666619;

%e a(5) = 12, 666666666619; etc.

%t Select[Range[2, 100000], PrimeQ[(2*10^# - 143)/3] &]

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Feb 04 2017

%E a(24)-a(25) from _Robert Price_, Mar 14 2018